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This randomized phase III trial studies how well graft-vs-host disease (GVHD) prophylaxis works in treating patients with hematologic malignancies undergoing unrelated donor peripheral blood stem cell transplant. Giving chemotherapy and total-body irradiation before a donor peripheral blood stem cell transplant (PBSCT) helps stop the growth of cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving total-body irradiation (TBI) together with fludarabine phosphate (FLU), cyclosporine (CSP), mycophenolate mofetil (MMF), or sirolimus before transplant may stop this from happening.

All patients receive FLU intravenously (IV) over 30 minutes on days -4 to -2 followed by 2-3 Gy TBI on day 0.

ARM 0: Patients receive CSP orally (PO) twice daily (BID) on days -3 to 96 with taper to day 150 and and sirolimus PO once daily (QD) on days -3 to 150 with taper to day 180. Arm removed as of 14-Sep-2011

ARM I: Patients receive CSP orally (PO) twice daily (BID) on days -3 to 96 with taper to day 150 and MMF PO three times daily (TID) on days 0-29 and then BID on days 30-150 with taper to day 180.

ARM II: Patients receive CSP as in Arm I and sirolimus PO once daily (QD) on days -3 to 150 with taper to day 180. Patients also receive MMF PO TID on days 0-29 and then BID on days 30-40. MMF will then be discontinued without taper unless GVHD or disease relapse/progression occurs.

TRANSPLANTATION: Patients undergo allogeneic PBSCT on day 0 following the TBI.

After completion of study treatment, patients are followed up periodically.

A Randomized Phase III Study to Determine the Most Promising Postgrafting Immunosuppression for Prevention of Acute GVHD After Unrelated Donor Hematopoietic Cell Transplantation Using Nonmyeloablative Conditioning for Patients With Hematologic Malignancies: A Multi-center Trial

Patients receive FLU IV over 30 minutes on days -4 to -2. Patients also receive CSP PO BID on days -3 to 96 with taper to day 150 and MMF PO TID daily on days 0-29 and then BID on days 30-150 with taper to day 180. Patients undergo allogeneic PBSCT on day 0 following the TBI.

Patients receive FLU and CSP as in Arm I and sirolimus PO QD on days -3 to 150 with taper to day 180. Patients also receive MMF PO TID on days 0-29 and then BID on days 30-40. MMF will then be discontinued without taper unless GVHD or disease relapse/progression occurs. Patients undergo allogeneic PBSCT on day 0 following the TBI.

Incidences of Acute Grade II-IV GVHD, Exclusive of GVHD That Occurs as a Result of Alterations to Immunosuppressive Therapy in Response to Relapse or Progression [ Time Frame: At day 100 post-transplant ]

Number of patients who developed acute GVHD post-transplant. aGVHD Stages

Diarrhea is graded 1 - 4 in severity. Nausea and vomiting and/or anorexia caused by GVHD is assigned as 1 in severity. The severity of gut involvement is assigned to the most severe involvement noted. Patients with visible bloody diarrhea are at least stage 2 gut and grade 3 overall.

Number of patients who developed chronic extensive GVHD post-transplant. The diagnosis of chronic GVHD requires at least one manifestation that is distinctive for chronic GVHD as opposed to acute GVHD. In all cases, infection and others causes must be ruled out in the differential diagnosis of chronic GVHD.

Incidences of Grade III-IV Acute GVHD [ Time Frame: Up to 100 days ]

Number of patients who developed acute/chronic GVHD post-transplant. aGVHD Stages

Diarrhea is graded 1 - 4 in severity. Nausea and vomiting and/or anorexia caused by GVHD is assigned as 1 in severity. The severity of gut involvement is assigned to the most severe involvement noted. Patients with visible bloody diarrhea are at least stage 2 gut and grade 3 overall.

Number of Participants With Relapse/Progression [ Time Frame: Up to 1 year ]

Relapse/Progression criteria:

CML New cytogenetic abnormality and/or development of accelerated phase or blast crisis. The criteria for accelerated phase will be defined as unexplained fever >38.3°C, new clonal cytogenetic abnormalities in addition to a single Ph-positive chromosome, marrow blasts and promyelocytes >20%.

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Ages =< 50 years of age with hematologic diseases treatable by allogeneic HCT who through pre-existing medical conditions or prior therapy are considered to be at high risk for regimen related toxicity associated with a high dose transplant (> 40% risk of transplant related mortality [TRM]); this criterion can include patients with a HCT-comorbidity index (CI) score of >= 1; transplants should be approved for these inclusion criteria by the principal investigators at the collaborating centers and at the Fred Hutchinson Cancer Research Center (FHCRC); all children < 12 years must be discussed with the FHCRC principal investigator (PI) prior to registration

Ages =< 50 years of age with chronic lymphocytic leukemia (CLL)

Ages =< 50 years of age with hematologic diseases treatable by allogeneic HCT who refuse a high-dose HCT; transplants must be approved for these inclusion criteria by the principal investigators at the collaborating centers and at FHCRC

The following diseases will be permitted although other diagnoses can be considered if approved by Patient Care Conference (PCC) or the participating institutions' patient review committees and the principal investigators

Aggressive non-Hodgkin lymphomas (NHL) and other histologies such as diffuse large B cell NHL: not eligible for autologous HCT, not eligible for high-dose allogeneic HCT, or after failed autologous HCT

Failed to meet National Cancer Institute (NCI) Working Group criteria for complete or partial response after therapy with a regimen containing FLU (or another nucleoside analog, e.g. 2-Chlorodeoxyadenosine [2-CDA], pentostatin) or experience disease relapse within 12 months after completing therapy with a regimen containing FLU (or another nucleoside analog);

Failed FLU-cyclophosphamide (CY)-Rituximab (FCR) combination chemotherapy at any time point; or

Have "17p deletion" cytogenetic abnormality; patients should have received induction chemotherapy but could be transplanted in 1st CR; or

Patients with a diagnosis of CLL (or small lymphocytic lymphoma) or diagnosis of CLL that progresses to prolymphocytic leukemia (PLL), or T-cell CLL or PLL

Hodgkin lymphoma: must have received and failed frontline therapy

Multiple myeloma: must have received prior chemotherapy; consolidation of chemotherapy by autografting prior to nonmyeloablative HCT is permitted

Acute myeloid leukemia (AML): must have < 5% marrow blasts at the time of transplant

Acute lymphocytic leukemia (ALL): must have < 5% marrow blasts at the time of transplant

Chronic myeloid leukemia (CML): patients in 1st chronic phase (CP1) must have failed or be intolerant of tyrosine-kinase inhibitors (TKI); patients beyond CP1 will be accepted if they have < 5% marrow blasts at time of transplant

Myelodysplasia (MDS)/myeloproliferative syndrome (MPS): patients must have < 5% marrow blasts at time of transplant

Waldenstrom's macroglobulinemia: must have failed 2 courses of therapy

DONOR: FHCRC matching allowed will be grades 1.0 to 2.1: Unrelated donors who are prospectively:

Only a single allele disparity will be allowed for HLA-A, B, or C as defined by high resolution typing

DONOR: Donors are excluded when preexisting immunoreactivity is identified that would jeopardize donor hematopoietic cell engraftment; this determination is based on the standard practice of the individual institution; the recommended procedure for patients with 10 of 10 HLA allele level (phenotypic) match is to obtain a panel reactive antibody (PRA) screens to class I and class II antigens for all patients before HCT; if the PRA shows > 10% activity, then flow cytometric or B and T cell cytotoxic cross matches should be obtained; the donor should be excluded if any of the cytotoxic cross match assays are positive; for those patients with an HLA class I allele mismatch, flow cytometric or B and T cell cytotoxic cross matches should be obtained regardless of the PRA results; a positive anti-donor cytotoxic crossmatch is an absolute donor exclusion

DONOR: Patient and donor pairs homozygous at a mismatched allele in the graft rejection vector are considered a two-allele mismatch, i.e., the patient is A*0101 and the donor is A*0102, and this type of mismatch is not allowed

DONOR: Only filgrastim (G-CSF) mobilized PBSC only will be permitted as a hematopoietic stem cell (HSC) source on this protocol

Exclusion Criteria:

Patients with rapidly progressive intermediate or high grade NHL

Patients with a diagnosis of chronic myelomonocytic leukemia (CMML)

Patients with refractory anemia with excess blasts (RAEB) who have not received myelosuppressive chemotherapy i.e. induction chemotherapy

Fertile men or women unwilling to use contraceptive techniques during and for 12 months following treatment

Females who are pregnant or breast-feeding

Patients with active non-hematological malignancies (except non-melanoma skin cancers) or those with non-hematological malignancies (except non-melanoma skin cancers) who have been rendered with no evidence of disease, but have a greater than 20% chance of having disease recurrence within 5 years; this exclusion does not apply to patients with non-hematologic malignancies that do not require therapy

Fungal infections with radiological progression after receipt of amphotericin B or active triazole for greater than 1 month

Cardiac ejection fraction < 35% (or, if unable to obtain ejection fraction, shortening fraction of < 26%); ejection fraction is required if age > 50 years or there is a history of anthracycline exposure or history of cardiac disease; patients with a shortening fraction < 26% may be enrolled if approved by a cardiologist

The FHCRC PI of the study must approve of enrollment of all patients with pulmonary nodules

Patients with clinical or laboratory evidence of liver disease would be evaluated for the cause of liver disease, its clinical severity in terms of liver function, and the degree of portal hypertension; patients will be excluded if they are found to have fulminant liver failure, cirrhosis of the liver with evidence of portal hypertension, alcoholic hepatitis, esophageal varices, a history of bleeding esophageal varices, hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction evinced by prolongation of the prothrombin time, ascites related to portal hypertension, bridging fibrosis, bacterial or fungal liver abscess, biliary obstruction, chronic viral hepatitis with total serum bilirubin > 3 mg/dL, or symptomatic biliary disease

Karnofsky scores < 60 or Lansky Score < 50

Patient has poorly controlled hypertension and on multiple antihypertensives

Human immunodeficiency virus (HIV) positive patients

Active bacterial or fungal infections unresponsive to medical therapy

All patients receiving antifungal therapy voriconazole, posaconazole, or fluconazole and who are then randomized to ARM 2 must have sirolimus reduced according to the Standard Practice Antifungal Therapy Guidelines

The addition of cytotoxic agents for "cytoreduction" with the exception of tyrosine kinase inhibitors (such as imatinib), cytokine therapy, hydroxyurea, low dose cytarabine, chlorambucil, or Rituxan will not be allowed within three weeks of the initiation of conditioning

DONOR: Donor (or centers) who will exclusively donate marrow

DONOR: Donors who are HIV-positive and/or, medical conditions that would result in increased risk for G-CSF mobilization and harvest of PBSC